Trying to login to WP admin panel I get ‘‘ERROR: An error was encountered while trying to authenticate. Please try again’’. Trying to login from Plesk Panel of my host I get ''405 Not Allowed’’. I have not changed anything from my last login. Please advise.
mysites.gr
test.mysites.gr
This is likely coming from the origin, and not Cloudflare.
But you can easily test this: temporarily disable the Cloudflare proxy 
(ie change DNS to 
mode) and test your site. If the problem persists, then it’s from either your Plesk server or WordPress setup… and not Cloudflare.
Thank you GeorgeAppiah.
It was working perfectly for years now…
But I did disable the proxy to check and them I had problem with the SSL certificate.
The thing is that now, after some time, I tried again to login and it worked (proxy enabled).
So it must have been something temporary from Cloudflare.
Thanks anyway.
Then you need to fix this first. A site needs to work fine on HTTPS before you use Cloudflare, otherwise you have exactly these issues.